In our paper, adjoint equation \((p,q)\)  is deduced by the relation between \(y^1\)  and \(x^1\)  due to its coupling at \(T\)  with \(y_T=\phi (x_T)\) . However, when we degenerate to the case \(y_T=y_T\)  being deterministic, it is natural that \(p\)  disappears.
Then Theorem REF  reduces to Theorem 4.4 of Peng [1]}, the local maximum principle of completely observed case for decoupled FBSDEs with the following relations:
\(\begin{aligned}&h_t=q_t,\ m_t=p_t,\ n^1_t=k_t,\\&\mathcal {H}_u(t,\bar{x},\bar{y},\bar{z}^1,h,m,n^1,\bar{u})=H_u(\bar{x},\bar{y},\bar{z},\bar{u},p,k,q,t),\end{aligned}\) 
